CN1238775C - 用于采用范围控制的多变量预测控制的最佳控制器的设计方法 - Google Patents
用于采用范围控制的多变量预测控制的最佳控制器的设计方法 Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
Abstract
在包括至少一个被操作变量及至少一个受控变量的系统中提供了一种用于增强的过程控制的方法。得到被操作变量的预定约束及被操作变量的当前值。控制器装入确定最佳控制器的参数,这些参数是脱机计算出来的。为了确定这些参数将定义过程最坏情况的模型的单一最小-最大陈述,该过程将结合具有最佳情况的控制器来操作。单一最小-最大陈述将转换成最小问题形式的规范表达,最小问题的结果解答就是该参数。计算对于今后预定数目的点的控制变量的新值,以使这些控制变量的值在预定范围中,由此获得结果控制器的最佳坚固性。被操作变量也被计算以在预定约束内,当可控制时控制变量落在预定的范围内。从多个解中选出最大增强的一个解。然后对被操作变量进行调整以使过程控制系统将受控变量的值驱至计算值上。
Description
技术领域
本发明涉及控制系统,更具体地涉及用于采用范围控制的增强的(robust)多变量预测控制(RMPC)技术的最佳控制器的设计方法。
背景技术
在现代过程控制系统中,目前已使用了许多技术,它们应用控制过程变量到预定设置点的模型预测控制技术。通常设置点是系统操作者对一个或多个设置点值的最好估计。当过程被控制到一个设置点上时,控制器可能不会获得最佳控制性能,尤其是在过程/模型失配的情况下。为了进一步增强控制系统的整体性能,故希望设计一种明确地处理设备或模型不定性的控制器。
发明内容
本发明提供了一种用于采用范围控制的多变量预测控制的过程控制系统的控制器的设计方法。该控制器被设计来操作为最坏情况的过程。因此就获得了对于该过程的最佳控制器,及在实际过程不是最坏情况的过程的情况下,控制器的性能将比预期的还好。
因此,本发明提供了一种用于采用范围控制的增强的多变量预测控制(RMPC)技术的最佳控制器的设计方法。一包括至少一个被操作变量及至少一个受控变量的过程控制系统提供了一种用于增强的过程控制的方法。被操作变量及受控变量的预定约束及被操作变量的当前值被获得。该控制器装有确定最佳控制器的参数,这些参数是脱机计算出来的。为了确定这些参数,将定义该过程的最坏情况模型的单一最小—最大陈述,该过程将结合一最佳情况的控制器来操作。单一最小—最大陈述被转换成最小化问题形式的规范表达,最小化问题的结果的解答就是该参数。计算用于今后预定数目的点的受控变量的新值,以使这些受控变量的值在预定范围中,因此获得结果控制器的最佳坚固性。被操作变量也被计算以在预定的约束内,当可控制时受控变量落在一预定的范围内。从多个解答中选出最增强的一个解答。然后对被操作变量进行调整,以使过程控制系统将受控变量的值驱至计算值上。
因此本发明的一个目的是提供一种确定最佳控制器的方法,以便在最坏情况的过程系统上获得最控制性能。
当结合以下的说明及附图时,将会使本发明的上述和另外的目的变得更加明白,其中相似的符号表示相似的部分,及这些附图将成为本申请的一部分。
附图说明
图1表示用于对本发明的二维最小—最大问题解答的图形说明图。
具体实施方式
在本发明的采用范围控制的增强的多变量预测控制器(RMPC)中,以脱机方式获得了一种最佳控制器设计,它能提供在最坏情况过程上取得最佳控制性能的最佳控制器。采用范围控制的RMPC的详细说明可以参考美国专利US5,351,184来得到,该专利已转让给本申请的同一受让人,它将在理解本发明所需的程度上结合于此作为参考。
在可采用本发明的过程控制系统中。一控制器具有多个输出,它们作为输入变量u被连接到过程。例如可包括多个可被控制的元件,如阀,加热器---。该过程的过程变量包括温度、压力、电平、流量---它们支配着产品的质量。输入变量(或被操作变量)u被定义为:
及输出变量(或受控变量)CV被定义为:
因此,该过程是一个具有K个被操作变量及几个受控变量的动态过程P(m)。受控变量(CV)包括n1个被调节的CV,n2个被约束的CV及n3个被优化的CV。控制器的范围控制函数被公式化来处理上述三种情况,并完全被描述在上述美国专利US5,351,184中。
本发明的增强控制设计的一个目的是明确地处理设备或模型的不定性。概括地说,希望控制器维持预定水平的性能,甚至当过程变化时也是如此。增强控制设计既保证了增强的稳定性又保证了增强的性能。前者保证了对于在以不定性为特征的一组的所有设备,该控制器是稳定的,而后者则保证对于该组设备能期望得到合理的性能。最佳增强的控制设计问题的通常形式为:
min max J(Q(p),m)
Q m
它表达该问题是寻求一个控制器Q,它将在所有的参数m上使最坏性能J减至最小。性能J恒定为涉及控制器Q10,过程P20及模型M30的复合函数。稳定性和性能问题又限制了设计。为了保证增强的稳定性,模型的不定性限制了互补灵敏度函数的最大奇值。增强的性能的要求通过结构化的奇值限制了设计。
在传统的意义上,增强的控制设计设法直接解决用于控制器Q10的最小—大问题。因为限制处理实际上是所有工业过程控制器的最重要方面,传统的增强设计不能直接地应用。但是,具有两个关键的有助于公式化RMPC设计的增强的控制概念。第一个是使用最大奇值来建立RMPC控制器上的范数界限,它被完整地描述在上述专利中。第二个是使用用于控制器综合的最小—最大原理,它将被讨论于下。
过程P(m)20被参数化,例如增益,时间常数,时间延迟(或处理时间)均是未知的但被定义以使一参数m位于最高及最低界限之间:
m≤m≤
m
模型M30是过程P20的“描述”。但是,在模型30及过程20之间经常有某些程度的失配。如果给出一个模型,就能确定出该RMPC控制器(如上述专利中由范围控制算法(RCA)所述)。由于模型及过程之间的失配,故使用了不同的变量。下面,过程P用字母m表示,模型M用字母P表示。为了进一步改善用通用形式来表述的控制器:
min max J[Q(p),m]
Q(p) m
其中m为过程参数(对于该过程的参数m无事可做)及p为模型的参数。
本发明要解决的问题是:
第一)通过使误差空间J最大化找出最坏的设备(过程),与使用哪个控制器无关。具有一高—低界限(
m≤m≤
m)中的m的参数组合以使得过程将引起最大故障。
第二)寻找将工作于最坏过程的最佳控制器。
这就定性地描述了要解决的问题。这不是一个最大问题。这也不是一个最小问题。它是一个最小最大问题(MIN-MAXPROBLEM)。最小—最大(min-MAX)是一个单算符。
该算符的形式为:
注:最小化P而不是Q(P),因为Q是一个因变量。一旦P被选出,使用RCA可以知道Q。
该要解决的问题的通用形式变为:
min max J[Q(p),m]
p m
其条件为:
m≤m≤
m
p≤p≤
p
m在其范围中是离散的,因此:
m[m1,m2,m3,....mn]
则该通用形式为:
min max Ji[Q(p)]
p i
式中Ji=J〔Q(p),mi〕。
上述最小—最大问题可重新以典型形式通过加入变量α来陈述,它表达为:
min α
p,α
其条件为:
Ji(Q(p))-α≤0。
该规范形式可以等效地由图形说明表示。该规范形式更易于求解,因为这一个最小问题。参照图2,它表示用于解二维最小—最大问题的图形说明(但它也同样可用于3维,---)。从函数域中抽出的任何点PA可被映入函数空间。Ji是P的函数,m1解析为J1及m2解折为J2:
在函数域中的所有点映入一定形状(仅作为例子,在该函数空间中表示为一椭圆)。现在找出点x,因为它产生出最小的J1,J2值。这就是α的值,因为J1-α=0及J1-α=0。从Jα转换Ji的反函数(从函数空间返回到函数域)就得到了解P。(在函数空间中所划出的正方形用于各个α值,与转换的图形(这里是椭圆)的曲线接触的正方形的角即为α的值)(注意:这是仅为一个α的值—单值,这就是为什么使用正方形)。
该解点得出P并使用在上述专利中所述的RCA,确定出控制器。用于获得改善性能的模型M(P)也被得到。
虽然所描述的是本发明优选实施例所考虑的内容,但显然,在不偏离本发明基本精神及范围的前提下对其可作出许多改变及修改。因此希望,附设权利要求书可覆盖落在本发明精神内的所有这些变化和修改。
Claims (1)
1、在过程控制系统中,一种提供过程的增强的控制方法,该系统具有提供对过程的增强的控制的控制器,该过程还具有至少一个被操作变量及至少一个过程变量,该方法包括下列步骤:
a)给控制器装入确定最佳控制器的参数,这些参数的脱机计算包括步骤:
i)定义该过程的最坏情况模型的单一最小-最大陈述,该过程结合具有最佳情况的控制器来操作;
ii)将所述单一最小-最大陈述转换成相应的最小化表达,该相应的最小化表达是规范的单一最小-最大陈述;及
iii)解最小化问题获得结果的解,该结果的解即为这些参数;
b)使该增强的控制初始化,以具有被操作变量和受控变量的预定约束;
c)获得该被操作变量及过程变量的当前值,所述过程变量相应于该过程的测量参数;
d)计算对于今后预定数目的点的过程变量的新值,以便具有在预定范围中的这些过程变量的值,由此获得结果控制器的最佳坚固性,被操作变量在预定约束内,当可控制时这些过程变量落在一预定范围内;否则使对过程变量的约束干扰保持为最小;
e)从多个解中,选择一个最大增强的解;及
f)根据最大增强的解,控制该过程。
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US08/415,881 US5572420A (en) | 1995-04-03 | 1995-04-03 | Method of optimal controller design for multivariable predictive control utilizing range control |
US08/415,881 | 1995-04-03 |
Publications (2)
Publication Number | Publication Date |
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CN1180422A CN1180422A (zh) | 1998-04-29 |
CN1238775C true CN1238775C (zh) | 2006-01-25 |
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CNB961930403A Expired - Fee Related CN1238775C (zh) | 1995-04-03 | 1996-04-01 | 用于采用范围控制的多变量预测控制的最佳控制器的设计方法 |
Country Status (6)
Country | Link |
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US (1) | US5572420A (zh) |
EP (1) | EP0879443B1 (zh) |
JP (1) | JP3843128B2 (zh) |
CN (1) | CN1238775C (zh) |
DE (1) | DE69622047T2 (zh) |
WO (1) | WO1996031813A1 (zh) |
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